Pattern recognition



9 Sheets-Sheet 1 Filed April 1'7, 1961 INVENTOR mm 64 M0 ATTORNEYS JZWgm 423M "H 5 l l H N :22: I11 m Ill I, 5 N x T .H 54 e2 :2 GE 3E :25

Jan. 22, 1963 GAMQ PATTERN RECOGNITION 9 Sheets-Sheet 2 Filed April 17,1961 Jan. 22, 1963 H. GAMO v 3,074,634

PATTERN RECOGNITION Filed April 17, 1961 9 Sheets-Sheet s SEQUENCER IJan. 22, 1963 GAMO 3,074,634

' PATTERN RECOGNITION Filed April 17, 1961 9 Sheets-Sheet 5 Jan. 22,1963 Filed April 17, 1961 H. GAMO PATTERN RECOGNITION 9 Sheets-Sheet 7Jan. 22, 1963 H. GAMO PATTERN RECOGNITION 9 Sheets-Sheet 9 Filed April17, 1961 5 an 2 M $58 :5: sa g M 2m W\ 4 United States Patent 3,074,634PATTERN RECOGNITION Hideya Gamo, Katonah, N.Y., assignor toInternational Business Machines Corporation, New York, N.Y., acorporation of New York Filed Apr. 17, 1961, Ser. No. 103,432 17 Claims.(Cl. 235-151) This invention relates to apparatus for recognizingpatterns, and more particularly, for generating signals representingsaid patterns.

The field of pattern and character recognition has assumed primaryimportance in modern data processing equipment, especially whereautomatic checking and tabulation of merchandise is desired. Heretofore,most recognizing circuits involved an optical beam or the like forscanning across the face of a character or pattern in the fashion of thewell-known television cameras. This method, besides being somewhat slow,depends upon almost perfect registration of the pattern with respect toa fixed coordinate system which is part of the scanning mechanism.Little or no rotation or transverse translation of the pattern, withrespect to this coordinate system, can be tolerated by these prior artcircuits. Therefore, their utility is almost nil for such applicationsas identification of merchandise which is borne on moving conveyers orthe like, or where such merchandise is somewhat haphazardly placedwithin the recognizing area.

The present invention obviates many of the above problems by providing amethod and means for sensing certain characteristics of particular kindsof patterns, which characteristics are substantially invariant withrespect to pattern registration within certain limits. Furthermore, thepatterns may assume forms that have coded significance, particularlybinary, and they may have either a self-luminous or light reflectivecharacteristic. The invention has particular application in areas suchas the recognition of grocery items, or the like.

It is therefore an object of the present invention to providerecognition means for symmetrical patterns in the shapes of circularconcentric bands, square concentric bands, parallel bands, and the like.

Another object of the present invention is to provide means to measurethe absolute value of the square of the Fourier transform of the lightdistribution at said pattern.

A further object of the present invention is to provide logical methodsand means for generating digital signals epresenting each patternscanned.

Still another object of the present invention is the recognition ofself-luminous or coherently lighted symmetrical patterns having binaryrepresentations, regardless of their registration within limit withrespect to the scanning mechanism.

These and other objects of the invention will become apparent during thecourse of the following description, which is to be taken in conjunctionwith the drawings, in which:

FIGURE 1 shows a block diagram of one embodiment of the presentinvention for recognizing self-luminous patterns, together with severaltypes of patterns that may be recognized;

FIGURES 2 and 3 disclose details about the patterns and theircorresponding detectors;

FIGURES 4 and 5 show a first embodiment for measuring the invarientcharacteristics of a self-luminous pattern;

FIGURE 6 shows a second embodiment for measuring the invariantcharacteristics of a self-luminous pattern;

FIGURE 7 shows a detail of FIGURES 8 and 9;

FIGURE 8 shows a first embodiment for calculating "ice the binary bitsrepresenting a pattern from its measured invariant characteristics;

FIGURE 9 shows a second embodiment for calculating binary bits from themeasured pattern invariant characteristics; and

FIGURE 10 shows a block diagram of a second embodiment of the inventionfor coherently illuminating a reflecting pattern and measuring itsinvariant characteristics.

Referring first to FIGURE 1 of the drawings, a block diagram of oneembodiment of the invention is shown, together with example of thedifferent shapes of patterns which may be recognized. A self-luminouspattern is placed at pattern plane 1 so that light therefrom may bedirected through a focusing lens 2 to impinge upon a detection plane 3.The three pattern shapes shown below pattern plane 1 in FIGURE 1indicate some of several kinds of patterns which may be recognized bythe circuitry of the present invention but are not to be construed as alimitation thereof. For example, a pattern 6 consisting of circularconcentric bands may be used, each having binary significance. Each bandin this pattern may be composed of such material that light is generatedtherefrom which impinges upon the detection plane 3. The two dark bandsof pattern 6 indicate that they are so constructed. Patterns 8 and 10are also shown. Pattern 8 comprises a set of rectangular concentricbands, each having a binary order value associated therewith as inpattern 6. In pattern 10, a series of parallel bands are shown, and thepattern is symmetrical about the center band. All three of the patterns6, 8 and 10 are symmetrical around at least one of its coordinate axes.

Positioned at detection plane 3, which is to the right of lens 2, aredetecting elements D D D upon which impinge the light from a pattern atplane 1. Detection plane 3 is the back focal plane of lens 2, thisdistance being indicated by f. Directly beneath detection plane 3 inFIGURE 1 are shown the shape of the light detectors thereat which mustbe used to detect the different kinds of patterns employed at plane 1.For example, light detector 7 comprises a set of concentric detectorrings spaced apart from each other as shown by distances d. The lightdetector 7 has a shape similar to that of pattern 6 with which it isused. In like fashion, detector 9 is in the shape of a series ofconcentric squares spaced apart from each other. Detectors 9 would beused when the patterns 8 appear on pattern plane 1. When the patternstake the shape of 10, the detectors 11 are as shown and consist of aseries of parallel lines spaced apart from each other. Other symmetricalpatterns of different shapes can also be sensed, by correspondinglyshaped detectors. The structure of the light detectors will subsequentlybe explained in detaihhowever, each may generally consist of a thinphotoconductive element responsive to light which generates a currentproportional to its intensity. In a further embodiment of the invention,the detectors merely consist of opening in the detection plane 3 throughwhich light from the object may be selectively passed so as to strike asingle photocell therebehind. Only one shape of pattern may normally beemployed at the pattern plane for any particular shape light detector atdetection plane 3 for the most reliable operation.

Each of the detctor elements measures the intensity of the lightincident thereon and produces a signal proportional thereto. Thesesignals may be represented by the terms I I I where there are N +1detector elements present, including the detector at the center of thedetection plane which is required when the pattern is selfluminous. Thesignals are transmitted to unit 4 which combines them in a mannerhereinafter to be described in order to produce certain translationalinvariant signals B B B whose subscripts relate them to each of thedetectors D D D Since the patterns appearing at pattern plane 1 areself-luminous, each signal B appearing from unit 4 represents theabsolute value of a particular mutual coherence factor 1 which will besubsequently defined. These output signals B are next applied to circuit5 which contains logic for mathematically combining the E signals withvalues permanently stored thercin to produce a number of binary bits, aa a (1;; representing the binary significance of the pattern at patternplane 1. As noted previously, each concentric band, square, or bar of apattern has a different binary order significance, with its variable ubeing 1 in the preferred embodiment if light is transmitted therefrom tothe detection plane.

Referring now to FIGURES 2 and 3, the general theory of operation of thedevice in FIGURE 1 will be explained. For purposes of this discussion, apattern having the shape of circular concentric bands is assumed to beplaced at the pattern plane 1. Two of these patterns are illustrated inFIGURES 2a and 2b. A five ring pattern, including the center circle, isshown, although patterns containing any number n of the rings may beused. Each of the rings has a binary order significance such that theouter most ring represents order 2, while the innermost ring (circle)represents order 2 The binary order significance of the other ringsprogresses toward the center from 2 to 2 as the rings become smaller. Inthe embodiment of FIG- URE 1, a ring is formed of a self-luminousmaterial, such as phosphor, only if the binary variable a of that orderis to have a value of 1. Otherwise, a ring is formed of nonluminousmaterial if the variable is to have a value of 0. The self-luminouscharacteristics of phosphor are evident under irradiation by ultravioletlight. Other self-luminous material may also be employed for thepatterns, and, as will subsequently be described in connection with FIG-URE l pattern rings may also be formed of reflecting material which isilluminated by coherent light.

In FIGURES 2a and 2b, any rings formed of the selfluminous material areshaded. Thus, in FIGURE 2a, only the outermost ring possesses thisself-luminescent quality. Since this ring has binary order 2significance, the binary variable a associated with this order has avalue of 1. All other variables a through a, have a value of 0, becausethe rings having under significance 2 through 2 respectively, are madeof non-luminous material. The pattern of FIGURE 2a may therefore berepresented by a binary number which has a decimal significance of 1. InFIGURE 2b, three rings are formed of self-luminous material so thatbinary variables [14,a3, and d have the value 1. Therefore, the patternof FIGURE 2b may be represented by the binary number having a decimalsignificance of 21. In the case where the pattern of FIGURE 2a is beingsampled by the circuits of FIGURE 1, the output binary number appearingfrom calculating unit 5 will take the form of 00001, while a sample ofthe FIGURE 2b pattern will make this output have the form of 10101.Thus, the invention, as generally shown in FIGURE 1, will produce abinary number having a value unique to the pattern being scanned.Furthermore, this number is produced as a result of observing the wholepattern at the same time, rather than by sequentially sensingincremental areas therein as is done in much of the prior art.

Since the patterns shown in FIGURES 2a and 2b have a number of ringsequal to 5, then the maximum number of ring combinations is 2 or 32.This includes the situation where none of the rings of a pattern haveselflurninosity, such that the pattern is represented by 00000, ordecimal 0. For patterns having N number of bands 4 corresponding to thenumber of detector rings D the total combination available is 2*.

The radii of the rings in the patterns of FIGURES 2a and 2b arerepresented by r r r 1' and a, where a is the maximum radius. Thesedimensions are shown in FIGURE 2a. For purposes of the present analysistwo specific kinds of patterns will be considered. One kind is thatwhere each ring has the same width, i.e.,

r :r r =r -r =r r =otr However, this geometry is not essential to theoperability of the invention, and a second kind of pattern is that whererings of equal area are employed. In this second case, the followingrelationships must hold:

In other words, r /2r r /3r r =2r and a=\/5r However, the proceduresspecifically developed for the above two kinds of patterns can beextended for patterns where the rings have dimensional relationshipsother than the above. The only criterion, as regards the presentinvention, is that the pattern be symmetrical with respect to at leastone of its X or Y center axes. This means that indicia representing abinary order has a mirror image on the opposite side of the X or Y axes,or both.

Turning now to FIGURE 3, a description will be given of the detectorsused for sensing light emitted from the patterns of FIGURES 2a and 212.As shown in FIG- URE 1, these detectors are placed at the back focalplane of lens 2, and should be of a shape similar to the pattern whichis to be recognized. Since the present discussion is limited toconcentric rings, the detectors in FIGURE 3 are also of this shape.However, it is to be understood that this particular shape of patternand detector is not to be construed as a limitation of the invention.For the five ring patterns as shown in FIGURES 2a and 211, there areprovided five detector rings D through D together with a center detectorD These detector rings may take several forms, depending upon the methodused for generating the output signals B, through B shown in FIG- URE 1.For example, each detector D may comprise a thin annular ring ofphotoemissive material which produces a current I proportional to theintensity of light falling thereon. The center detector D is also madeof such material. Alternatively, each detector ring may comprise anannular slit in an opaque plane surface, together with a set of lightgates positioned adjacent to said slit so as to allow the transmissionof light therethrough only when said set of light gates is selected bycontrol logic. In this second scheme, the transmitted light is incidenton a single detector placed behind the back focal plane, so that currentis produced proportional to the light intensity. These two forms ofdetector rings Will be more fully described in connection with FIGURES4, 5, and 6. However, it should briefly be mentioned here that thecenter detector D is not required when the patterns are made ofreflective material instead of self-luminous phosphor. This distinctionwill become apparent later on, and for the present, only self-luminouspatterns are under consideration.

In FIGURE 3, the width W of each detector ring D may be extremely smallwhen compared with the distance d between adjacent rings. The radius ofeach ring, as measured from the center detector D is represented by 3 pp p and p Formulas for calculating these radii will subsequently begiven in the discussion to follow.

Several equations will now be derived which will explain the operationof the present invention. A detailed description of the structure shownin FIGURES 4 and 9 then follows, wherein a combination of circuits isshown for accomplishing the functions defined by said equations.

In FIGURE 20, first assume that the location of each point source ofself-luminous light on the pattern can be expressed in terms of arectangular coordinate system having X and Y axes with an origin at thepattern center.

Now select a specific point M on said pattern having coordinate valuesof x and y. Also assume that the location of each point at the detectionplane can be expressed in terms of a rectangular coordinate systemhaving U and V axes with the origin at the center where detector D isplaced, as in FIGURE 3. Select a first detection point N havingcoordinate values of u and v on said detection plane, and a seconddetection point D having coordi nates O, 0. It has been found that aFourier transformation of the light intensity distribution I at point Min the pattern yields the so-called mutual coherence factor I asmeasured between points D and N at the detection plane; Thus,

The mutual coherence factor I' v) may also be defined in the followingmanner.

r (u ,v) VG) .0) hltfl where V (t) represents the light Wavedisturbances due to the pattern point source M which are measured at thecenter of the detection plane,

represents the complex conjugate of the light wave disturbances whichare measured at point N of the detection plane, and represents the timeaveraging (or integration) of the product. For a detailed analysis ofthe significance of Equations 1 and 2, reference may be made to Chapterof Principles of Optics, Born and Wolf, Pergamon Press (1959).

The mutual coherence factor T v) is generally a complex number in theform of a-l-ib, which has an absolute value If in the form of x/a -i-bAssume now that the pattern of FIGURE 2a is now shifted with respect tothe X and Y coordinate system, so that point M has coordinates of x+Ax,y-l-Ay. A different mutual coherence factor P v) will now be measured atpoints N and D of the detection plane. The relationship between I v) andT v) is given by the following equation.

The absolute value of P is therefore equal to the absolute value of Ii.e., |I Therefore, it may be appreciated that regardless of patternregistration with respect to the detection plane (within certain limits,the absolute value of the mutual coherence factor I is the same when itis measured between the same two points at the detection plane. Anotherway of stating the above is to say that the absolute value of the mutualcoherence factor at the back-focal plane of lens 2 is independent of anyshift of the self-luminous circular pattern along the object plane 1, oreven in a direction parallel to the optical axis. This fact is employedin the present invention for the purpose of accurate pattern recognitionregardless of pattern translation with respect to the detector plane.This feature is especially useful where accurate positioning of thepattern is not possible or impractical, as might be the case wheremerchandise is marked with a pattern or patterns to represent its price,etc.

The mutual coherence factor P v) may also be represented in its polarcoordinate form by where p is the distance of point N from the center ofthe detection plane, and 0 is the angle made with a reference line. Thequantity 1 may likewise be represented by R where r is the distance fromthe center of the pattern, and is the angle. When the intensitydistribution I of a complete ring of points at radius r is considered,then 1 reduces to 1 since is continuous from 0 to 21r. At the detectionplane, an analogous transformation may be made from This latter termrepresents the mutual coherence function measured between the center ofthe detection plane, and a detector ring having a radius p. Equations 1and 3 above may be extended to prove that 9) is equal to the Fouriertransform of I(r), and that its absolute value i (Mi is independent ofpattern registration. Furthermore, when considering a complete patternhaving a number of concentric self-luminous bands, each with a finitewidth, a mutual coherence function b) may be measured at the detectionplane whose absolute value is dependent only upon the binary combinationof said self-luminous bands, but not upon the pattern registration. Forany given pattern, however,

i Mi will also vary according to the value of p at which a detector ringis located.

In the embodiment shown in FIGURE 3, detector rings D1, D2,D3,D4, and D5exist at discrete radii p1, p p3, p4, and p with respect to the centerdetector D Therefore, the values i (P )iii (/=2)iii P i:i (p )i: and ifi wi are respectively measurable between these detector rings and thecenter detector D In FIGURE 1, the signals B B B B (where N=5 for thepresent discussion) represent the values of ]1 etc., when the pattern isself-luminous. These signals B B B .B are generated in unit 4 bycombining signals 1 ,1 I I in a manner subsequently to be described.

For any given pattern, the above five mutual coherence factors, whichare obtained from the detector rings in FIGURE 3, have the followingmatrix relationship to the five binary bit values a a a a and a; whichnumerically represent the pattern being sampled.

:1: 1M I 5: Anal 1: A o i AM 1; A a. :1: A a

2i: i w I i A24 4 zs a :i: 22 2 i 21 1 :i: A20 4)- WW i z :l: 34 4 i A333 Aszllz :l: 31 1 :1: Aso o l mp i A44 4 :i: 43 3 :l: 42 2 i An l i A400 it 1 7ml 54 4 i 53 6 :l: 52 2 :1: fil l i 50 0 In Equations 4 above,each of the a a a variables has a binary value equal to +1 or 0,depending upon the pattern being sampled. Each A value, where n is theparticular detector sampling ring and k is the binary order indicationof the associated variable a is equal to the value of the mutualcoherence factor of a pattern having only the u ring self-luminous.Thus, the value of i I tp l for any pattern is To illustrate the above,assume that the value of matrix 4 is to be represented in terms of the Aand a values, when a pattern is being sampled having a binaryrepresentation of 00101. This particular mutual coherence factor maythen be represented as :l: i a u b ll '1? According to line 2 ofEquation 4,

i im i i 21 4 23 3 i 22 2 i 21 1 :i: 201 0 The respective mines of a a aa and (t are 00101 Therefore, the terms :A cq, ifi a and :A a ofEquation 6 are all equal to zero. In the remaining terms :A is equal tothe value of i l (cpl for a pattern having only one self-luminescentring, This particular value may be represented by th n in like fashion,the matrix element :A is equal to the value of i l q/ 1i for a patternhaving only one self-luminescent ring, that represented n This may berepresented as i E r-M 3] Therefore, Equation 6 becomes ii :1 :1 ,0 9} il o (p i It i n t li In the invention as shown in FIGURE 1, the problempresented is: given the measured values of and the :A matrix elements,calculate the binary variables 0 a a a a This may be done easily byfirst determining the inverse matrix values A y and then precedingaccording to the following equations:

a: i Ali- 1 1 1) I a Ali-In ut i ir ine! i M i Aio| P s i 2F inPp] i efi tp I I1". ez l w i 21 inal i n I win The inverse matrix values A maybe calculated from the original matrix values A by well-knownmathematical techniques. These values are stored within unit 5 for usewith the measured values of which are represented in the figures bysignals B The variables a through a, are calculated therein in themanner prescribed by matrix 8.

As has been indicated throughout the above discussion, the measuredvalues may have either positive or negative significance, depending uponthe binary significance of the pattern. If the improper sign is given toone or more of these values when they are used in matrix 8, then one ormore of the binary variables [lg-(Z will have a value other than +1 or0. In the present invention, it is impossible to initially determine theproper signs for the measured values Therefore, a particular sign isassumed for each, and the calculated variables 4 through a, are examinedto see if all are valid. If any are invalid, i.e., equal to binaryvalues other than 1 or 0, then a different combination of signs isemployed, until a valid output is obtained. This output then represents,in binary fashion, the particular pattern under observation. Due to thelack of precision when measuring the values where A is the FourierBessel coefficient, a is the maximum pattern radius,

r 0( on is a Bessel function of order zero, and A is the nth positiveroot of J (x)=0. These roots A may be obtained from any well-known tablesuch as page 748 of Watson,

Theory of Bessel Functions. Since The) is the Fourier transform of I(r),then where J is the derivative of J (x) at xzx and K=21F x where is thewave length of the self-luminous light from the pattern.

Equation 10 may be transformed into the following:

where C is a function of Kozp and is equal to on" 0( P) 0 on) P) onWhere Ka =Mn for example, the function C 0 equal to 1, while all otherfunctions C 0 equal zero. Therefore, Equation 11 becomes where men rosand A is the first positive root of the function J (X) :0.

In like manner,

Therefore, the detector rings D are placed at radii It may be seen fromEquation 14 that when the pattern is very large or if the wave length ofthe self-luminescent light is small, then p will be small. Theoretically1,, is

generally independent of the focal length if of lens 2 in FIGURE 1.However, in practice the spatial frequency of the pattern may have to beconsidered, so that Equation 14 above is modified as below.

u pitf Assume first that the pattern has concentric rings all of equalwidth, and that only the outermost band is selfluminous so that :1,while :1 through 41 all equal zero. The width of this band is a= /5 a,where a. is the maximum radius of the pattern. Equation 16now'becomes""" Where I(r) is considered equal to 1 between the limits ofEquation 17, this equation can be written as P L 7 2mm Kp r)d7 19 whichreduces to 2J (Kap 2J1(().8Ka r385= Kama 81 (08mm (19 where J (x) is aBessel function of the first order. By

using the values of p as determined by Equations 14 or 15, the values ofwm wz) owo wo and ot 's) may be calculated, which are the values ofmatrix elements A A A A and A in Equation 4.

Equations similar to '19 may be developed for the remaining A matrixelements. For example, in a pattern where (1 :1, and a a a a all equalzero, the width 0 the band a, is /sa- /s1x, and

From Equation 20, the values of A A A A and A may be derived by usingthe values of 1 p 12 p and p from the sampling theorem.

For matrix elements A A A A and A insert values of pH into thefollowing:

(0.4)Kap For matrix elements A A24, A34, A and A To illustrate thepractical use of Equations 19 through 23, Tables 1, 2, and 3 shown belowgive actual values for i-Ank, i-A and :B,,, respectively, when thefollowing conditions are observed. A first condition is that the productKat in the Equations is everywhere set equal to 1 in order to avoidhaving to select specific values for K and a. A second condition, whichis implied from the first, is that the value 1rrx in the Equations isdisregarded. A third condition is that Equations 19 through 23 do notinclude, and the tabulated values therefore do not reflect, the effectsof different kinds of detectors about which more will be said at a latertime. The fourth and last condition is that the specific values of pused in the calculations are obtained from Equation 14. Therefore, inview of the foregoing four conditions, the values shown in Table 1 aresomewhat universal in that they can be used for a great variety of fivering equal width patterns and their corresponding detectors whenmodified by constants of proportionality. As modified by the aboveconditions, Equation 19, for example, is written thus:

amp 1 Pn) O 8 1( Pn) 24 In Table 1 below, the calculated values formatrix elements A are therefore given by the values of Table 1 (EqualWidth) (A24) (A21) (A22) (A21) (A20) 0. 03420750 0. 04619826 0. 033514070. 19703550 0. 06313878 (A34) (A35) (A32) (A11) (A40) (510 (A5) (All)(410 (410 0. 01793893 0. 03710698 0. 02097157 0. 02194642 0. 06317820(A54) (A54) (A52) (A51) (A50) Table 2 (Equal Width) 1? 1? ll 1? il (4,?)(Ag; (5;; (A5) (A5} Table 3 (Equal Width) at 21-, :11 :10 B1 B2 B3 B4 B50 0 0 0 1 0. 0.06313878 0.06790198 0.06317820 0.05196863 0 0 0 1 0 0. 0.10703550 0. 04237965 0. 02194642 0. 04439320 0 0 0 1 1 0. 0. 17017429011028165 --0. 04123178 0. 00757542 0 0 1 0 0 0. 0. 03351407 0. 061737340. 02097157 0. 03520270 0 0 1 0 1 0. 0. 09665287 0. 00616464 0. 042206630. 08717134 0 0 1 1 0 0. 0.14054959 0. 01935768 0. 04291799 0. 009190500 0 1 1 1 0. 0. 2030ss3s 0. 04351430 0. 02020021 0. 04277813 0 1 0 0 00. 32 0. 04010320 0. 01258735 0 03710608 0. 02 133223 0 1 0 0 1 0.13733257 0. 01694052 0. 05531463 0. 10028517 0. 02763640 0 1 0 1 00120782856 --0. 06083724 0. 02979230 0. 01516055 (106872543 0 1 0 1 1 0,24262781 --0. 12397603 0. 09769429 0. 07833876 0 01675680 0 1 1 0 0 0.23135334 0. 01268418 0. 07432470 0. 01613540 (101087047 0 1 1 0 1 0.26615258 0. 05045460 0. 00642271 -0. 07931361 0. 06253911 0 1 l 1 0 0.33664958 0. 09435132 0. 03104503 000581101 0. 03352273 0 1 1 1 1 0.37144782 0. 15749010 0. 03595694 0. 05736719 0. 01844590 1 0 0 0 0(103879716 0. 03420750 0. 02677955 0. 01793893 0. 00922103 1 0 0 0 10107359641 0. 02803128 0. 09468154 0. 04523926 0. 06118967 1 0 0 1 00.14409240 0.07262800 0.06915921 0 03988535 0 03517216 1 6 0 1 10.13596679 0. 13706120 0 02329285 0 01679646 1 0 1 0 0 0.000693420.03495779 0 03891050 0 0 1442374 1 0 l 0 1 0.0624-1536 0. 03294419 002426770 009639238 1 0 1 1 0 0.1063420S (100742187 0 06085692 0.00003053 1 0 1 1 1 0.16948087 0.07532385 0 00232128 005199917 1 1 0 0 00108040577 001419219 0 01016803 0. 01511119 1 1 0 0 1 001726603 0.08209419 0 08234624 003685744 1 1 0 1 0 0.02662973 0.05657186 0 00277837--0.05950439 1 1 0 1 1 0.08976852 0.12447385 0 06039982 0. 00753576 1 11 0 0 004689169 -0. 04754514 0 00180352 0. 02009151 1 1 1 0 1 0.01024700 002035684 0. 00137407 07 07200015 1 l 1 l 0 -0. 06014381 0.00510548 0. 02374994 0. 02430169 1 1 1 1 1 0. 41024499 0. 12328260 0.06273650 0. 03942626 0. 02766694 In Table 3 above, the values for B B BB and B are seen to be different for each of the thirty-two uniquecombinations available with a five ring pattern. These B values areinvariant characteristics of the pattern and are measured by apparatussubsequently to be described, wherein the case 01" self-luminouspatterns, they respectively represent the five mutual coherence factors|P p 111K113, iil p l, ink/19E, and illmml previously defined.

The general Equation 16 may also be used in developing formulas forcalculating the values of matrix elements A for a five ring patternwhere the rings all have equal areas. For this case, the outer radius rof each ring can be expressed in terms of the maximum pattern radius 0:as follows: r =cz\/ /5; r =a /-/s; r =a /s; and r4 l1'\/ l 5 Therefore,the formula for determining elements A A A35 A and A may be written inthe form of Equation 18 as follows, with the limits of integration beingthe width or" hand n in terms of a:

Table 4 (Equal Area) R 1 ,.2 7 5 (A14) (A13) (A12) (An) (A n) 1 l (2017112274 011000595 (107492670 (103789456 0. 00723203 which reduces to 06 1 70 0012 0 71: 0 9 0 1 20 0 ()(Acn) 4 775 45' -.7s75 -.s7e -.1001721( l D) A 1( Pn) 26 s (p (A30 (A10 7:) (2171) (An) 91: 2/45 1,4100158850 0. 04851957 0. 03320015 0. 05609526 0. 02351000 Similarly,the equations for the remaining matrix ele- 1-14, (A13) (An) 41) A11)mans An: are developed as above 4102021102 (103057589 0. 01053570001317000 uozsssosa 2 FT (A11) 57) (A52) 5) 501 PG (p 1) [4/5m -g/5m l(27) 0.00611744 0. 02077501 003ss2757 0. 024 77711 0. 02105502 Table 5(Equal Area) (.177) (A79) (A7; (17,) (A 3. 68361500 7. 08773798 8.65961254 6. 70042771 3. 10430000 (119,) (A) (A7,?) (A5) (A5, 4. 3754420324. 71592259 76. 90386787 92. 11770058 39. 03714050 (A (A73 7 7 73 s.93020020 69. 10424014 109. 49760628 -21s. 28442383 -110.4000s3s0 (A7;(17;) (A77) (A73) (A77) 11. 41080630 108. 02333503 287. 96886826 350.46870041 10s. 76925087 their degree of opaqueness to light. shutter Dmay be mechanical in nature for controlling the passage of light througha slit.

Table 6 (Equal Area) at a: a: a1 30 B1 B2 B3 B4 B5 In FIGURE 4 of thedrawings is disclosed one embodiment whereby the measurement of thevalues ool may be accomplished. These circuits may be used as unit 4 inFIGURE 1'. FIGURE 4 shows a pictorial view of the detection (back focal)plane of FIGURE 1 at which an opaque screen 68 is placed having a seriesof concentric annular slit-s 69 through 73 correspond in ,next innermostannular slit 69 has associated therewith a light shutter D Shutters D DD D are likewise associated with annular concentric slits 70, 71, 72,and 73, respectively. A light shutter D may comprise a series ofannularly arranged Kerr electro-optical cells, which are responsive toan electrical signal for varying Alternatively, a

Shutters D through D are selectively opened and closed by means ofsignals emanating from a control unit 30, the structure of which willlater be described.

A single photo-detector 3 1 is placed on a line normal to center shutterD and at the image plane behind the opaque screen 68 in FIGURE 4. Thisphoto-detector 31 is on the opposite side of screen 68 from the patternplane 1 in FIGURE 1, and is responsive to light from the pattern beingtransmitted through any of the opened slits, such that its out-putsignal is proportional to the total intensity stirring thereon.

Between photo-detector 31 and center shutter D is placed a device 65which, when actuated by a signal from control unit 30, shifts the phaseof anylight coming through center hole 74 by ninety degrees before itreaches photo-detector 31. Such a device may consist of the standardoptical onequarter wave plate which is selectively inserted into thepath of the beam. The output of photo-detector 31 is applied to gates3-2, 33, 34, and 35, which in turn feed respective storage circuits 36,37, 38, 39. Gates 32 through 35 are selectively energized by controlsignals from unit in order to respectively store in units 36 be defined.

reference may be made to An Aspect of Information Before describing theremaining circuitry in FIGURE 4, an analysis will be made of the use towhich the signals from photo-detector 31 are put. Initially, only thelight shutter D is opened to admit light from the pattern to passtherethrough and fall on detector 31. A signal 1 is generated by thisdetector which is proportional to the intensity of the incident lightthereon. Next, a shutter D is opened and shutter D closed, so thatdetector 3 1 generates a signal I Shutters D and D are then both opened,and the resulting photo-detector signal is represented by I Whileshutters D and D are both opened, the one-quarter wave plate 63 isactivated and operates upon the light passing through D to shift itsphase so that a signal I is generated by 31. The two signals I and I areto be defined as follows:

represent the real and imaginary parts of the mutual coherence factorTherefore, the value i P0 11) I may be ascertained by taking the squareroot of Equation 35. For a complete explanation of the above theory,

Theory In Optics, Hideya Gamo, IRE International Convention Record 1960, pages 189-203.

Returning now to FIGURE 4, the outputs from store units 36 and 37 areapplied to a summing network 40 where they are added together. Theoutput from 49 is next inverted (changed in sign) by 44 and applied toanother summing network 45. The other input to adder "i5 is applied fromeither store unit 38 or 39 in accordance with which of the gates 41 or42 is conditioned by control signals from unit 30. Thus, adder 49 addstogether I and I with this sum being successively subtracted from I andI which are stored in units 38 and 39, respectively. The components inadder network 45 may be proportioned so that the outputs therefrom areactually one-half of the differences I -(Z +I and I,, -(I +I in order tocomply with the requirements of Equations 33 and 34, respectively. Theoutputs from adder 45, which are respectively equal to the real andimaginary parts of the mutual coherence factor are fed throughrespective gates 46 and 4-7 to store units 48 and 49. Thus, the realpart of the mutual coherence factor is initially stored in unit 43, andthen the imaginary part is stored in unit 49. The outputs from these twostorage units are subsequently transmitted via squaring units 50 and 51to the input of adder 52, which mechanizes the function of Equation 35.The output from adder 52 is then sent to a square root unit 64 whoseoutput is then applied to one of the storage units 55 through 58 viaassociated gates 59 through 63, respectively. The signal placed in oneof the units 54 through 58 thus represents the value of l mml and istermed B FIGURE discloses details of circuit 30 which generatcs signalsA through T used in FIGURE 4 to control the components therein. As willbe appreciated from the above discussion, only one set of signals I I Iand I can be generated at a time. For example, detector shutters D and Dmay be selectively opened singly and in combination to produce signals II I and I which then may be mathematically combined to produce at theoutput of store unit 54. Subsequently, detector shutters D and D may beoperated, followed by the pairs of shutters D D D D.- and D D in thisorder. Therefore, where there are five detector rings D through D theremust be five distinct cycles in order to obtain five sets of respectivesignals I 1;, I 1 through 1 I I I each of which is used to calculate therespective signals B, through B In practice, there need be only onemeasurement of I at the beginning of the recognition period since thissame value is used in all five cycles. However, for purposes ofstandardizing each cycle as much as possible, the apparatus of FIGURE 5causes shutter D to open for each of the above signal sets.

In FIGURE 5, two sequence circuits 8-1) and 81, respectively designatedI and II, cooperate in order to successively generate pairs of signalsBP, C-Q, D-R, ES, and FT, each pair being unique to the cycles in whichsignals B through 8;, are generated, respectively. Sequence I providesduring each of the five cycles, successive signals on eight outputconductors 1 through 8, there being only one signal present at a time.Sequencer II provides, during each of the five cycles, a differentsignal on but one of its output conductors 1 through 5. Sequencer I isstepped each time that it receives a step pulse (generated by anoscillator or the like) at terminal 82-, but Sequencer II requires thepresence of both a step pulse and a signal from conductor v 8 (SequencerI) at AND gate 84 in order to change 16 its condition. Thus, SequencerII is stepped once for each eight steps of Sequencer I, which in turnrecycles to its step 1 after completing its step 3.

Output conductor 1 of Sequencer I is connected to OR gate 85 to generatethe control signal A each time a signal appears thereon. In addition, asignal H is produced at this time. From FIGURE 4, it will be seen thatsignal A opens shutter D thus producing I from photo-detector 31, whilesignal H conditions gate 32 to pass I into store 36. These twooperations must occur during each of the five cycles mentioned above.Conductor 2 of Sequencer I is connected to a set of OR gates 88 through90 for purposes of energizing one terminal of each of a set of AND gates91 through 95, respectively, which in turn respectively, produce signals8 through E. The other terminal of each AND gate 91 through 95 isenergized by a dilferent one of the output conductors from Sequencer II,such that only one of the signals B through F can be present during eachcycle. Since these signals respectively open shutters D through D it isseen that only one shutter D together with shutter D can be operatedduring a cycle. Output conductor 3 of Sequencer I is connected in commonto OR gates 85 through 90, as is output conductor 4. Signals appearingon either one of these conductors, therefore, open simultaneouslyshutter D and a shutter D,,, the latter depending upon which conductorof Sequencer II is energized in the cycle. Sequencer I conductor 4 alsoproduces signal G for energizing the one-quarter wave plate 65.Therefore, the first four steps of Sequencer I occurring each cycleresults in the successive generation of signals I I I and I byphoto-detector 31, with the subscript n being determined by theparticular condition of Sequencer II in each cycle. In addition, steps 1through 4 of Sequencer I also generate signals H, J, K and L,respectively, to condition gates 32 through 35.

Continuing with the steps of Sequence I during each cycle, the signalsappearing in succession on conductors 5 and 6 cause gates 4146, and 4247to open. Since these arithmetic operations, represented by respectiveEquations 33 and 34, must be performed during each cycle, there is nocontrol exerted by Sequencer II over signals M and N. Conductor 7 ofSequencer I is con nected in common to AND gates 96 through 100, each ofwhich also has another input from a respective one of conductors 1through 5 of Sequencer II. Thus, when step 7 of Sequencer 1 occursduring each cycle, only one of the signals P through T is generatedaccording to the state of Sequencer II. Step 8 of Sequencer Isubsequently resets store units 36, 37, 38, 39, 48, and 49, to preparethem for the next following cycle when signals I 1 I and I s are to begenerated and stored. As previously described, the signal on conductor 8also prepares AND gate 51 to pass a step pulse to Sequencer II.

In FIGURES 4 and 5, the details of each component functionally describedare well-known in the prior art, particularly in analog and digitalcomputer technology. The system shown may be completely analog innature, or an analog to digital converter might be used if desired toobtain digital representations of the signals I I,,, I and I generatedby photo-detector 31, after which all mathematical operations thereonare carried out by wellknown digital components and circuits. For thesereasons, the details of FIGURES 4 and 5 will not be spelled out,inasmuch as it is within the skill of one versed in the art to constructthe system shown without exercise of invention.

A brief description will now be given of the operation of FIGURES 4 and5. At the beginning, stage 1 in Sequencer I is set on so that light gateD is energized to pass light from the pattern therethrough. Sequencer IIis also in its first condition. This light is detected by 31, and theoutput signal I therefrom is transmitted via gate 32 to storage unit 36where stored. It will be noted that stage 1 of Sequencer I is alsodirected to gate 32 appear the respective signals I through I "17 topass this signal to the appropriate store. Sequencer I is now stepped toits second stage which energizes shutter D to generate the signal I,from photo-detector 31. This value is transmitted via gate 33 to store37. Stage 3 of Sequencer I next opens both shutters D and D in orderthat 31 can generate the signal I which is to be stored in unit 38 viagate 34. At stage 4 of Sequencer I, the one-quarter wave plate 65 isenergized together, with shutters D and D so that the signal I may begenerated and stored in unit 39 via gate 35. At Step 5 of Sequencer I,gate 41 is energized to pass the output from store 38 to adder 45 whereit is summed with the negative value of the output from adder 40. Thus,the output appearing from adder 45 at this time is the real part of thecoherence factor I p which is thereupon stored in unit 48 via gate 46.Subsequently, stage 6 of Sequencer I causes the output from store 39applied to adder 45 and there summed with the negative output of adder40, with the result passing through gate 47 to store 49. The result fromadder 45 at this time is the imaginary portion of I p The outputs fromunits 48 and 49 are respectively squared in units 50 and 51, whoseoutputs are applied to adder 52 with the result being the value of !I pThe square root of this quantity is taken by unit 64, and passed throughgate 59 to store 54, where it is available as signal B having theuniversal values shown in Table 3 or 6 if five ring equal area or equalwidth patterns are at the pattern plane. Stage 8 of Sequencer I nextresets the indicated stores so that they are prepared to receive thesignals I I I I etc. next to be generated.

Upon Sequencer I recycling back to its step 1, Sequencer II is advancedto its step 2 in order to allow shutter D and gate 60 to be operated asSequencer I repeats its eight steps. Thus, the value ]I is placed inStore 55 at the end of the second measuring cycle, which is subsequentlytermed B In measuring cycles 3, 4, and 5, similar operations result invalues |I p |I p and ]I p being stored in units 56, 57, and 58,respectively.

Figure 6 of the drawings discloses alternative apparatus for generatingsignals B -B when the patterns are self-luminous. This structureutilizes the Hanbury Brown-Twiss effect which is disclosed in TheProceedings of the Royal Society of London, vol. A242, pages 300-324(1957), and vol. A243, pages 291-319 (1957). In these publications, theauthors state the general proposition that when two light beams from acoherent or partially coherent source are respectively incident on twophotodetectors at respective positions 1 and 2, the correlation betweenthe signals generated by said photo-detectors is proportional to thesquare of the absolute value of the mutual coherence factor of the beamsas measured at the photo-detector positions. The correlation between anytwo signals is found by integrating their product over a finite time.Thus, when the signals from two photodetectors are multiplied togetherand this product integrated the result is the correlation coefficient ofthe signals which is proportional to the value of lI l Apparatits isshown in these publications for performing the above describedcalculations, with the name intensity interferometer given thereto.

In'FIGURE 6, a group of concentric ring detectors D through D togetherwith a center detector D are placed at the back focal plane 115. Eachdetector ring D has a corresponding radius p calculated from thesampling Equations 14 or 15, and each is made of photo-conductivematerial such that when exposed to light, a signal (current I,,) isgenerated therein whose magnitude is proportional to the intensity ofthe incident light thereon. A

'group of conductors 116 through 121 are respectively connected one eachto detectors D through D whereon Signal I is applied to one input ofeach of a group of correlation circuits 122 through 126, while signals Ithrough I are respectively applied one each to the other inputs ofcorrelators 122 through 126. Each correlation circuit, as may beobserved from the details of correlator 122, is comprised of amultiplier unit 127 which continuously forms the product of inputsignals 1 and I,,, together with unit 128 for integrating said productwith respect to time. Such correlators are well-known in the prior art,although the above identified Hanbury Brown-Twiss publications may beconsulted for further details.

The outputs from correlators 122 through 126 are respectively applied tosquare root units 129 through 133, from which emerge respective signalsB through B Signals B, through B have representative values shown byTable 3 or 6 when five ring patterns of equal width or area are beingscanned.

In operation, a self-luminous pattern is placed at pattern plane 1 inFIGURE 1 and light therefrom falls on the detectors D through D inFIGURE 6. Signals I through I are thereby generated. Correlator 122 anddetectors D and D comprise a Hanbury Brown-Twiss intensityinterferometer which produces an output proportional to the value of[PUMP i.e., to the square of the absolute value of the mutual coherencefactor of the light beams incident at detectors D and D The square rootof this value is taken by unit 129.

In like manner, correlator 123 and detectors D and D; comprise anotherHanbury Brown-Twiss interferometer for generating the value va thesquare root of which is then taken by unit 130. Correlators 124, 125,and 126 respectively produce l oal l oml and wi since they also compriserespective parts of three more Hanbury Brown-Twiss interferometers.

When compared with FIGURE 4, it will be appreciated that the apparatusof FIGURE 6 produces signals B through B at the same time instead ofsequentially. However, it is also obvious that a'single correlator couldbe used in FIGURE 6' if one of its inputs were to be successivelyconnected with detectors D through D thereby resulting in an equipmentgain through loss of speed.

As previously noted in connection with Tables 1 through 6, the' valuesthere shown for 'A,', Agf and B -we're calculated without considering,among other things, the particular construction of the detectingmechanism. In FIGURE 4, the total wave amplitude of light passingthrough an open shutter D is equal to the wave amplitude at anincremental point thereon, multiplied by the detector circumference 211Since the intensity of .a beam is equal to the square of its waveamplitude, it is seen that the output of photo-detector 31 due to lightthrough shutter D is proportional to (21rp Therefore, since the squareroot of I OMI is obtained, the value 21r must be considered. In Tables 1through 6, the values there shown should consequently be multiplied bythe corresponding constants 21rp when the measuring apparatus of FIGURE4 is employed. However, in FIGURE 6, the wave amplitude of lightstriking each incremental area of a photo-detector D, causes thegeneration of a number of signals each proportional to the intensity ofthe light at corresponding areas. The sum of these signals over thecircumference 27Tp results in the final output I from detector D Again,since the square root of is taken, then the value 27rp must beconsidered, such that the corresponding values in Tables 1 through 6must be multiplied thereby when the measuring apparatus of FIGURE 6 isused. It should also be added here, however, that the detector ringsused with the correlators in FIGURE 6 can be modified so as to moreclosely resemble those used in FIGURE 4. For example, if concentricslits are provided at the detection plane, a separate bundle of Lucitetubes for each slit may be used whose ends are arranged adjacent eachother and completely around the slit to conduct the light fallingthereon to a respective photo-detector, which in turn is connected toone input of a correlator circuit. Thus, slits D through D would berespectively associated one with a group of five photodctectors, each ofwhich would be respectively connected one with the group of correlators122 through 126. A photo-detector would also be provided for the centerhole D which in turn would be connected to all of the correlators. Insuch a modified arrangement of FIGURE 6, the effect produced, as regardsthe summation of wave amplitude around the periphery of the slit beforethe light impinges on a photo-sensitive surface, is similar to thatobserved in connection with FIGURE 4. Therefore, where a singlephoto-detector together with light transmission conductors aresubstituted in FIGURE 6 for each ring of photo-conductive material, theconstants 21Tp should be used to accordingly modify the values in Tables1 through 6.

Before describing the circuits of FIGURES 8 and 9, which perform themathematical operations indicated by Equations 8, a brief analysis willbe made of the effect that the signs of the values l UIflI have on thecalculations. As can be discerned from Table 3 or 6, many of the l t nilvalues for different patterns must have a negative sign attributedthereto in order that the calculated hits 0 through a, fall within thevalid ranges of 0 or +1. However, the circuits of FIGURE 4 and FIGURE 6both measure the square of the absolute phase coherence factor n)l fromwhich the value l tml is calculated by a square root routine. Thus, theactual sign of IPUMI is not known since the actual measured value l molis obviously always positive. Therefore, in using the signals B fromFIGURE 4 or FIGURE 6, signs must be assumed for each and thecalculations performed. If one or more signs are incorrect, however,then one or more of the calculated hits n through a, will have a valueother than 0 or +1. If invalid bits are so obtained, then a differentsign for one or more of the signals B must be assumed, and thecalculations repeated. The changing of the sign combinations continuesuntil valid values for all bits ar through a; are obtained.

Since five signals B are obtained when recognizing the patterns shown inthe particular embodiments, it is seen that there could be a maximum ofthirty-two different sign combinations which range from +B +B +13 +134,+85 to "B1, 'B2, -B3, B4, -B55. A11 OI'dBI'IY procedure for changing thesign combinations would therefore be one in which a binary progressionis followed, i.e., then followed by However. in examining Tables 3 and6, it is noted that not all of the sign combinations are present, andthat patterns with different decimal significance may have the same signcombination for their B values. For example, in Table 3, the values B,through B have respective signs and for all of the following patterns,each expressed in decimal: 0, l, 3, 5, 7, 9, l5, 17, 19, 21, 23, 29, and31. Thus if this particular sign combination is assumed then valid bitsa through a, would be calculated if the pattern being sensed were any ofthe above, In like fashion patterns 6, 14, and 30 all produce B, throughB values having respective signs and Table 7 below gives in full thenumber of sign combinations required to recognize any one of thirty-twounique equal width concentric ring patterns, while Table 8 gives thenumber of sign combinations required to recognize a like number of equalarea patterns.

Table 7 (Equal Width) Number of Signs Step patterns recognized I3, I32B: B4 5 Table 8 (Equal Area) Number of Signs Step patterns recognized B1B2 B3 B In comparing Tables 7 and 8, it is noted that the value alwaysis positive. Furthermore, only eleven sign combinations are required torecognize all of the equal area patterns, whereas thirteen combinationsare necessary to insure that all of the equal width patterns arerecognizable. However, if the sign change sequence followed a straightbinary progression, then more steps would be required. It is alsointeresting to note that twenty-seven patterns can be recognized in thefirst six steps of Table 8 as compared to twenty-five patterns in thefirst six steps of Table 7. Therefore, given any particular binarypattern, the chances are that fewer calculation steps will be requiredfor its identification if said pattern has equal area rings.

FIGURE 8 discloses means for calculating binary bit values in accordancewith Equations 8 and Tables 2, 3, and 7 when self-luminous patterns withequal width concentric rings are to be scanned. The mode of operation inFIGURE 8 is parallel, in that all of the binary bits a a are generatedsimultaneously.

The signals B through B from FIGURE 4 or FIGURE 6 are respectivelyapplied via conductors 200 through 203 to pairs of gates 204205,206-207, 208209, and 210--211. Each gate 204, 206, 208, and 210 has itsout- 233m, or 23311- put respectively connected to conductors 212, 213,214, and 215 on which appear the signals labeled O O O and These gatespermit their input signals to appear on these output conductors withoutchange in magnitude or polarity. Each gate 205, 207, 209, and 211 isrespectively connected to inverters 217, 220, 221, and 222 which in turnare respectively connected to conductors 212 through 215. The functionof the inverters is to change the polarity, but not the magnitude, of asignal applied to their inputs. Signal B is applied directly to theconductor 231 and is consequently labeled 0 so as to correspond interminology with signals 0 through 0 Each of the gates 204 through 211is conditioned to pass their respective input signals B through B bymeans of signals appearing on associated conductors 223 through 230.Only one gate of each pair can be conditioned during a calculation cyclein accordance with the sign to be associated with the signals B throughB For example, if B; requires a minus sign for the step 1 calculation inTable 7, gate 205 is conditioned to pass +B via inverter 217, resultingin --B on conductor 212. Conversely, gate 204 is conditioned during step5 of Table 7 to allow the +3 signal to pass unchanged in polarity toconductor 212. Therefore, signals 0 through 0 are merely the signals Bthrough B with each having a polarity or as determined by theconditioned gate in each of the pairs. Inasmuch as no inverter isprovided in conductor 231, signal 0 is always +B The cycling means forchanging the signs of the numbers represented by the B through B signalsincludes a stepped sequence circuit 232 and a switching matrix generallyindicated by 234. For economy of time, the embodiment of FIGURE 8requires only a maximum of thirteen sign changing steps performed insequence in accordance with Table 7 for calculating the correct valuesof the binary bits a through (1 Thus, sequence circuit 232 has thirteenoutput conductors 233 numbered accordingly upon which appear signals insuccession, there being only one such line energized at any one time. Aterminal R is provided to reset circuit 232 to a condition such thatoutput conductor 1 is energized, while a terminal S is provided toreceive signals, each of which steps the circuit and energizes adifferent one of the output conductors in the sequence indicated bytheir numbers. Sequence circuit 232 may comprise any one of a number ofwell-known stepping circuits in the art, such as a rotary switch, a ringcounter, a binary counter with binary to decimal translation, or thelike.

Each conductor 233 is connected to approximate ones of conditionconductors 223 through 230 as is illustrated by a small circlesurrounding the junction of a vertical and a horizontal line. Figure 7shows an enlargement 'of the details within such a circle, for example,that at signal appearing on conductor 228 due to energization of 233cannot be applied to others of the vertical conductors 233 because ofthe back biasing on the diodes associated with these other conductors233. For example,

I a signal on 228 in the above instance cannot be applied to any of thevertical conductors 233, 233 233 233 Thus, the use of diodes or the likein matrix 234 provides isolation between the vertical conductors 233,and consequently between the horizontal conditioning conductors so thatnone will be energized that are not connected with a single energizedconductor 233.

I Output signals 0 through 0 are applied to the matrix of resistorsgenerally indicated by 235. In this matrix, each resistor R has asubscript nk which indicates that its value is determined by thecorrespondingly desginated A value in Table 2. Thus, resistor R has avalue corresponding to the value of A l, and so on. As is well known inthe art, the function of each resistor in matrix 235 is to efiectivelymultiply the sig nal applied thereto. In order to obtain negative valuesof certain A elements shown in Table 2, inverters 236 through 244 areinserted in circuit with resistors R R etc., which in turn have valuesdetermined by the absolute values of matrix elements A A51 1, etc.Although in practice only one inverter need be used for each of thesignals 0 through 0 a separate inverter is shown for each appropriateresistor in order to emphasize the negative quality of the individual Amatrix elements.

In accordance with the equations of matrix 8, groups of the resistorsare tied together at respective terminals 245 through 249 in order tosum together the appropriate B XA products in order to produce thebinary bits a through 41 For example, resistors R R R R R are connectedat terminal 245 such that the products 01R54, O2R53, O3R62, O4R51, andO5R5 are summed together. Since each of the above products yields asignal proportional to the products respectively, the resulting signalat junction 245 is indicative of binary bit a having a value of 1 or 10if the signs of the I functions (or B values) have been correctlyassumed. In like fashion, groups of resistor R R R34--R30, R24'R20, andR14R10 perform Similar multiply and add. functions on the signals 0through 0 so as to generate binary bits a through 12 at terminals 246through 249, respectively.

As hereinbefore explained, an incorrect sign for one or more of the 1functions results in a value other than 1 or 0 for one or more of thebits a through a Therefore, means are provided to see if each signalgenerated at terminals 245 through 249 is a valid one, i.e., that it hasa binary signifiicance of l or 0. In the embodiment of FIGURE 8, these 1and 0" bit detectors are duplicated for each terminal and are indicatedby blocks 250 through 259. Each 1 detector generates an output only ifthe signal applied thereto represents a binary 1, while each 0" detectorregards only to a signal representing binary 0. Detectors for generatingan output signal upon the detection of equality between an internalreference signal and an input signal are well-known, and theirconstruction will therefore not be described in detail. As beforementioned, however, it may be necessary to design each detector so thatthere is a small range of values around either 1 or O, or both, withinwhich a calculated bit is considered valid. This is to compensate forcomponent tolerances, etc.

If any of the signals appearing at terminals 245 through 249 areinvalid, i.e., fail to represent binary 0 or 1, then the combination ofsigns for E through B must be changed, and bits a through a;recalculated. This is performed in FIGURE 8 by means of a coincidencecircuit 260. The outputs from each pair of l and 0 detectors associatedwith the terminals 245 through 249 are ORED together and connected viarespective conductors 261 through 265 to respective inputs of circuit260. A signal is generated from circuit 260 only if signals aresimultaneously presented to all of its inputs. Thus, if both detectorsof any one of the pairs fails to produce a signal, no output is obtainedfrom circuit 260. For example, assume that neither detector 250 nordetector 251 generates a signal, thereby indicating that the a signalfrom terminal 245 is invalid. The absence of the signal on conductor 261prevents an output from 260 even through bits a through a., may be validas indicated by a signal appearing from one of the detectors

1. APPARATUS FOR RECOGNIZING A PATTERN COMPOSED OF INFORMATION BANDS EACH HAVING BINARY ORDER SIGNIFICANCE IN ACCORDANCE WITH THE LIGHT EMANATING THEREFROM, SAID APPARATUS COMPRISING IN COMBINATION: A FIRST SAMPLING POSITION AND A PLURALITY OF N SAMPLING POSITIONS SPACED APART FROM EACH OTHER AND FROM SAID FIRST POSITION, AT WHICH LIGHT FROM SAID PATTERN IS INCIDENT, MEANS RESPONSIVE TO THE INCIDENT LIGHT AT SAID FIRST SAMPLING POSITION TOGETHER WITH THE INCIDENT LIGHT AT EACH OF SAID N SAMPLING POSITIONS FOR GENERATING N SIGNALS RESPECTIVELY REPRESENTING THE ABSOLUTE VALUES OF THE FOURIER TRANSFORM OF THE LIGHT DISTRIBUTION AT SAID PATTERN, MEANS FOR STORING CALCULATED VALUES OF MATRIX ELEMENTS, MEANS FOR SELECTIVELY MULTIPLYING EACH OF SAID N SIGNALS BY DIFFERENT ONES OF SAID STORED MATRIX ELEMENTS, AND MEANS TO SELECTIVELY ADD CERTAIN OF THE PRODUCTS OF SAID MULTIPLICATION TO GENERATE EACH DIGIT OF A BINARY NUMBER REPRESENTING SAID PATTERN. 